# Prove of the complicated integral

1. Jan 16, 2012

### shayaan_musta

Hi experts!

How to prove this integral?

$\frac{2}{e^{5}}$$\leq$$\int$$\int_{D}$e$^{-(x^{2}+y^{2})}$dxdy$\leq$2
on
D=[0,1] and [0,2]

Here D is subscript of the 2nd integral.

I seriously have no idea how to start. I am 100% blank with this question.

2. Jan 16, 2012

### micromass

Staff Emeritus
What is the maximum/minimum value that $e^{-(x^2+y^2)}$ can attain??

3. Jan 17, 2012

### JG89

Why not just calculate the integral? The rectangle (0,1) x (0,2) is diffeomorphic to a circle (or the circle minus a set of measure zero) so use the change of variables theorem.